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題名 長壽風險下自然避險策略之探討:以英國Money-Back年金商品為例
A Discussion on the Natural Hedging Strategy In Longevity Risk─A Case of Money-Back Annuity
作者 張君瑋
Chang, Chun Wei
貢獻者 黃泓智<br>楊曉文
張君瑋
Chang, Chun Wei
關鍵詞 長壽風險
自然避險
商品內避險
免疫目標
Longevity risk
Natural hedging
Immunization goal
日期 2015
上傳時間 3-Aug-2015 13:23:08 (UTC+8)
摘要 在醫療與衛生技術飛快進步下,長壽風險目前已成為國際上普遍重視之議題,為因應死亡率改善所帶來之不確定性影響,壽險公司與退休基金也衍生出各種避險策略,近年來避險策略發展中當以自然避險為主軸,其中又可分為商品間避險與商品內避險法。一般市場上含有商品內避險概念的商品並不少見,如生死合險與還本型保險等,雖然商品內避險法有規避基差風險與免除因保險期間重新配置商品組合造成管理費用之優點,卻也存在無法因應實際死亡率做調整之缺點。因此本研究以英國Money-Back年金商品為例,採用存續期間配適法建構商品內避險最適組合,並配合現金流量分析自然避險策略的真實效果,提供未來壽險公司作為設計商品時之參考。
本研究發現採取商品內避險法時,壽險部分在保險期間後期會發生反轉現象,現金流量淨值波動方向變成與年金險一致,導致商品後期淨值波動過大,失去避險效果;本研究同時發現過去評估自然避險效果時普遍採用的淨值免疫指標存在缺陷,無法兼顧現金流量波動與破產機率。因此我們提出一種創新指標,同時考慮免疫理論中的三大免疫目標,研究結果顯示透過創新指標較能夠完整的評估整體自然避險效果,減少壽險公司於保險期間因現金流量波動劇烈所衍生之資金借貸成本,獲得更佳的避險效果。
With the improvement of medical and hygienic techniques, longevity risk has become the most important issue in the world. Life insurers and the pension provider propose various kinds of hedging strategies to cope with the uncertainty due to the improvement in mortality. In recent year, the development of hedging strategies focus on natural hedging, which can classified as the hedging strategies according to different insured policies or the same insured policy with survival benefit and death benefit. Endowment is a good example for the hedging strategy from the same insured policy. Although hedging from the same insured policy can avoid basis risk and decrease the cost from rebalance in the insurance period, it couldn`t adjust product portfolios by experienced mortality rates. In this paper, we attempt to analyze the natural hedging effect for the Money-Back annuity and use the immunization model to find the optimal collocation of insurance products and evaluate the effect of the natural hedging by cash flow method.
We find that life insurance will happened contrary effect in the later insurance period when we try to hedging from the same insured. The changes on the liability of life insurance become the same direction with annuity and lead to more uncertain in later insurance period; We also discover that the indicator which used to evaluate the effect of natural hedging in the past has some defect, so we propose a new indicator which include three immunization goals. We find the new indicator can evaluate the natural hedging effect completely, then it may can help life insurers to avoid the cost of capital due to the unstable cash flow.
參考文獻 Boardman, Tom. "Annuitization Lessons from the UK: Money‐Back Annuities and Other Developments." Journal of Risk and Insurance 73.4 (2006): 633-646.
Chan, Linus Fang-Shu, and Chenghsien Tsai. "Effective Duration Analyses on the Policy Reserves of Life Insurance." Journal of Financial Studies 20.1 (2012).
Coughlan, Guy D., et al. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness." North American Actuarial Journal 15.2 (2011): 150-176.
Cox, Samuel H., and Yijia Lin. "Natural hedging of life and annuity mortality risks." North American Actuarial Journal 11.3 (2007): 1-15.
Cox, Samuel H., Yijia Lin, and Shaun Wang. "Multivariate exponential tilting and pricing implications for mortality securitization." Journal of Risk and Insurance 73.4 (2006): 719-736.
Fabozzi, Frank J. Duration, Convexity, and Other Bond Risk Measures. Vol. 58. John Wiley & Sons, 1999.
Fong, Joelle HY, Olivia S. Mitchell, and Benedict SK Koh. "Longevity Risk Management in Singapore`s National Pension System." Journal of Risk and Insurance 78.4 (2011): 961-982.
Huang, Hong-Chih, Chou-Wen Wang, and De-Chuan Hong. "An Optimal Strategy of Natural Hedging for a General Portfolio of Insurance Companies."
Huang, Hong-Chih, Sharon S. Yang, "Hedging longevity risk for Insurance Companies Considering Basis Risk."
Lee, Ronald D., and Lawrence R. Carter. "Modeling and forecasting US mortality." Journal of the American statistical association 87.419 (1992): 659-671.
Macaulay, Frederick R. "Some theoretical problems suggested by the movements of interest rates, bond yields and stock prices in the United States since 1856." NBER Books (1938).
Melnikov, Alexander, and Yulia Romaniuk. "Evaluating the performance of Gompertz, Makeham and Lee–Carter mortality models for risk management with unit-linked contracts." Insurance: Mathematics and Economics 39.3 (2006): 310-329.
Mitchell, Daniel, et al. "Modeling and forecasting mortality rates." Insurance: Mathematics and Economics 52.2 (2013): 275-285.
Redington, Frank M. "Review of the principles of life-office valuations." Journal of the Institute of Actuaries (1952): 286-340.
Richter, Andreas, and Frederik Weber. "Mortality-Indexed Annuities Managing Longevity Risk via Product Design." North American Actuarial Journal 15.2 (2011): 212-236.
Wang, Jennifer L., et al. "An optimal product mix for hedging longevity risk in life insurance companies: The immunization theory approach." Journal of Risk and Insurance 77.2 (2010): 473-497.
描述 碩士
國立政治大學
風險管理與保險研究所
102358018
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102358018
資料類型 thesis
dc.contributor.advisor 黃泓智<br>楊曉文zh_TW
dc.contributor.author (Authors) 張君瑋zh_TW
dc.contributor.author (Authors) Chang, Chun Weien_US
dc.creator (作者) 張君瑋zh_TW
dc.creator (作者) Chang, Chun Weien_US
dc.date (日期) 2015en_US
dc.date.accessioned 3-Aug-2015 13:23:08 (UTC+8)-
dc.date.available 3-Aug-2015 13:23:08 (UTC+8)-
dc.date.issued (上傳時間) 3-Aug-2015 13:23:08 (UTC+8)-
dc.identifier (Other Identifiers) G0102358018en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/77191-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 風險管理與保險研究所zh_TW
dc.description (描述) 102358018zh_TW
dc.description.abstract (摘要) 在醫療與衛生技術飛快進步下,長壽風險目前已成為國際上普遍重視之議題,為因應死亡率改善所帶來之不確定性影響,壽險公司與退休基金也衍生出各種避險策略,近年來避險策略發展中當以自然避險為主軸,其中又可分為商品間避險與商品內避險法。一般市場上含有商品內避險概念的商品並不少見,如生死合險與還本型保險等,雖然商品內避險法有規避基差風險與免除因保險期間重新配置商品組合造成管理費用之優點,卻也存在無法因應實際死亡率做調整之缺點。因此本研究以英國Money-Back年金商品為例,採用存續期間配適法建構商品內避險最適組合,並配合現金流量分析自然避險策略的真實效果,提供未來壽險公司作為設計商品時之參考。
本研究發現採取商品內避險法時,壽險部分在保險期間後期會發生反轉現象,現金流量淨值波動方向變成與年金險一致,導致商品後期淨值波動過大,失去避險效果;本研究同時發現過去評估自然避險效果時普遍採用的淨值免疫指標存在缺陷,無法兼顧現金流量波動與破產機率。因此我們提出一種創新指標,同時考慮免疫理論中的三大免疫目標,研究結果顯示透過創新指標較能夠完整的評估整體自然避險效果,減少壽險公司於保險期間因現金流量波動劇烈所衍生之資金借貸成本,獲得更佳的避險效果。
zh_TW
dc.description.abstract (摘要) With the improvement of medical and hygienic techniques, longevity risk has become the most important issue in the world. Life insurers and the pension provider propose various kinds of hedging strategies to cope with the uncertainty due to the improvement in mortality. In recent year, the development of hedging strategies focus on natural hedging, which can classified as the hedging strategies according to different insured policies or the same insured policy with survival benefit and death benefit. Endowment is a good example for the hedging strategy from the same insured policy. Although hedging from the same insured policy can avoid basis risk and decrease the cost from rebalance in the insurance period, it couldn`t adjust product portfolios by experienced mortality rates. In this paper, we attempt to analyze the natural hedging effect for the Money-Back annuity and use the immunization model to find the optimal collocation of insurance products and evaluate the effect of the natural hedging by cash flow method.
We find that life insurance will happened contrary effect in the later insurance period when we try to hedging from the same insured. The changes on the liability of life insurance become the same direction with annuity and lead to more uncertain in later insurance period; We also discover that the indicator which used to evaluate the effect of natural hedging in the past has some defect, so we propose a new indicator which include three immunization goals. We find the new indicator can evaluate the natural hedging effect completely, then it may can help life insurers to avoid the cost of capital due to the unstable cash flow.
en_US
dc.description.tableofcontents 第壹章 緒論 1
第一節、研究動機 1
第二節、研究目的 3
第貳章 文獻回顧 4
第一節、英國Money-Back商品介紹 4
第二節、自然避險策略 5
一、存續期間(Duration) 6
二、免疫策略(Immunization Strategy) 6
三、壽險業自然避險策略 7
第參章 研究方法 10
第一節、模型假設 10
一、死亡率模型:Lee-Carter模型 10
二、存續期間模型 11
第二節 研究方法介紹 14
一、保單內容假設 14
二、目標函數 14
第肆章 數值分析 18
第一節 情境1:w1=1 (淨值免疫效果) 19
一、平均存續期間 19
二、效率存續期間 20
三、目標函數 22
第二節 情境2:w2=1 (現金流量免疫效果) 33
第三節 情境3:w1=0,w2=0 (到期日免疫效果) 36
第四節 綜合指標 40
第伍章 結論與建議 44
參考文獻 46
zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102358018en_US
dc.subject (關鍵詞) 長壽風險zh_TW
dc.subject (關鍵詞) 自然避險zh_TW
dc.subject (關鍵詞) 商品內避險zh_TW
dc.subject (關鍵詞) 免疫目標zh_TW
dc.subject (關鍵詞) Longevity risken_US
dc.subject (關鍵詞) Natural hedgingen_US
dc.subject (關鍵詞) Immunization goalen_US
dc.title (題名) 長壽風險下自然避險策略之探討:以英國Money-Back年金商品為例zh_TW
dc.title (題名) A Discussion on the Natural Hedging Strategy In Longevity Risk─A Case of Money-Back Annuityen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Boardman, Tom. "Annuitization Lessons from the UK: Money‐Back Annuities and Other Developments." Journal of Risk and Insurance 73.4 (2006): 633-646.
Chan, Linus Fang-Shu, and Chenghsien Tsai. "Effective Duration Analyses on the Policy Reserves of Life Insurance." Journal of Financial Studies 20.1 (2012).
Coughlan, Guy D., et al. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness." North American Actuarial Journal 15.2 (2011): 150-176.
Cox, Samuel H., and Yijia Lin. "Natural hedging of life and annuity mortality risks." North American Actuarial Journal 11.3 (2007): 1-15.
Cox, Samuel H., Yijia Lin, and Shaun Wang. "Multivariate exponential tilting and pricing implications for mortality securitization." Journal of Risk and Insurance 73.4 (2006): 719-736.
Fabozzi, Frank J. Duration, Convexity, and Other Bond Risk Measures. Vol. 58. John Wiley & Sons, 1999.
Fong, Joelle HY, Olivia S. Mitchell, and Benedict SK Koh. "Longevity Risk Management in Singapore`s National Pension System." Journal of Risk and Insurance 78.4 (2011): 961-982.
Huang, Hong-Chih, Chou-Wen Wang, and De-Chuan Hong. "An Optimal Strategy of Natural Hedging for a General Portfolio of Insurance Companies."
Huang, Hong-Chih, Sharon S. Yang, "Hedging longevity risk for Insurance Companies Considering Basis Risk."
Lee, Ronald D., and Lawrence R. Carter. "Modeling and forecasting US mortality." Journal of the American statistical association 87.419 (1992): 659-671.
Macaulay, Frederick R. "Some theoretical problems suggested by the movements of interest rates, bond yields and stock prices in the United States since 1856." NBER Books (1938).
Melnikov, Alexander, and Yulia Romaniuk. "Evaluating the performance of Gompertz, Makeham and Lee–Carter mortality models for risk management with unit-linked contracts." Insurance: Mathematics and Economics 39.3 (2006): 310-329.
Mitchell, Daniel, et al. "Modeling and forecasting mortality rates." Insurance: Mathematics and Economics 52.2 (2013): 275-285.
Redington, Frank M. "Review of the principles of life-office valuations." Journal of the Institute of Actuaries (1952): 286-340.
Richter, Andreas, and Frederik Weber. "Mortality-Indexed Annuities Managing Longevity Risk via Product Design." North American Actuarial Journal 15.2 (2011): 212-236.
Wang, Jennifer L., et al. "An optimal product mix for hedging longevity risk in life insurance companies: The immunization theory approach." Journal of Risk and Insurance 77.2 (2010): 473-497.
zh_TW